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A study of meshless methods for optimization of cathodic protection systems. (English) Zbl 07110390
Summary: Over the last decades, several computer codes have been developed aiming at the full 3D simulation of cathodic protection (CP) systems. CP is a technique applied to prevent corrosive processes and the main goal of the simulation has been to predict the degree of corrosion control achieved. Many pioneering works allowed for the successful application of the boundary element method (BEM) to CP systems. The aim of the present contribution is to introduce a brief overview of cathodic protection system modelling, including some numerical simulations. Mathematical formulations for the electrochemical potential problem are proposed, considering the following meshless methods: the method of fundamental solutions (MFS) and a meshless local Petrov-Galerkin (MLPG2) procedure. The meshless methods performances are evaluated comparing their results with a direct BEM solution procedure. The meshless applications are original first time attempts of such formulations to corrosion problems and cover a lot of practical situations found in actual cathodic protection applications.
MSC:
 74 Mechanics of deformable solids 65 Numerical analysis
Keywords:
BEM; corrosion; truly meshless methods
HYBRJ; minpack
Full Text:
References:
 [1] Koch, G.; Varney, J.; Thompson, N.; Moghissi, O.; Gould, M.; Payer, J., International measures of prevention, application and economics of corrosion technologies study, (2016), NACE International IMAPCT Report: NACE International IMAPCT Report NACE International, Houston, TX [2] Cicek, V., Cathodic protection: industrial solutions for protecting against corrosion, (2013), John Wiley & Sons Inc: John Wiley & Sons Inc New York, United States [3] Fleck, R. N., Numerical evaluation of current distribution in electrical systems, (1964), University of California [4] Doig, P.; Flewitt, P. E.J., A finite difference numerical analysis of galvanic corrosion for semi-infinite linear coplanar electrodes, J Electrochem Soc, 12, 2057-2063, (1979) [5] Fu, J. W., A finite element analysis of corrosion cells, Corrosion/NACE, 38, 5, 9-12, (1982) [6] Montoya, R.; Rendon, O.; Genesca, J., Mathematical simulation of cathodic protection system by finite element method, Mater Corros, 56, 404-411, (2005) [7] Brebbia, C. A., The boundary element method for engineers, (1978), New York: Pentech Press: New York: Pentech Press London and Halstead Press · Zbl 0414.65060 [8] Brebbia, C. A.; Telles, J. C.F.; Wrobel, L. C., Boundary elements techniques: theory and applications in engineering, (1984), Springer-Verlag: Springer-Verlag Berlin Heidelberg New York · Zbl 0556.73086 [9] Cheng, A. H.D.; Cheng, D. T., Heritage and early history of the boundary element method, Eng Anal Bound Elem, 29, 268-302, (2005) · Zbl 1182.65005 [10] Brebbia, C. A., The birth of the boundary element method from conception to application, Eng Anal Bound Elem, 77, iii-x, (2017) · Zbl 1403.65002 [11] Danson, D. J.; Warne, M. A., Current density/voltage calculations using boundary element techniques, Proceedings of the NACE conference. Los Angeles, USA, (1983) [12] Telles, J. C.F.; Mansur, W. J.; Wrobel, L. C.; Marinho, M. G., Numerical simulation of a cathodically protected semisubmersible platform using PROCAT system, Corrosion, 46, 513-518, (1990) [13] Brasil, S. L.D. C.; Telles, J. C.F.; Miranda, L. R.M., On the effect of some critical parameters in cathodic protection systems: a numerical/experimental study, (Munn, R. S., (1991), American Society for Testing and Materials), 277-291 [14] Santiago, J. A.F.; Telles, J. C.F., On boundary elements for simulation of cathodic protection systems with dynamic polarization curves, Int J Numer Methods Eng, 40, 2611-2622, (1997) · Zbl 0887.65126 [15] Kim, Y. S.; Kim, J.; Choi, D.; Lim, J. Y.; Kim, J. G., Optimizing the sacrificial anode cathodic protection of the rail canal structure in seawater using the boundary element method, Eng Anal Bound Elem, 77, 36-48, (2017) · Zbl 1403.74181 [16] Santos, W. J.; Brasil, S. L.D. C.; Santiago, J. A.F.; Telles, J. C.F., A new solution technique for cathodic protection systems with homogeneous region by the boundary element method, Eur J Comput Mech, 1, 1-15, (2018) [17] Kupradze, V. D.; Aleksidze, M. A., Aproximate method of solving certain boundary-value problems, Soobshch akad nauk Gruz SSR, 30, 529-536, (1963) [18] Mathon, R.; Johnson, R. L., The approximate solution of elliptic boundary-value problems by fundamental solution, SIAM J Numer Anal, 14, 638-650, (1977) · Zbl 0368.65058 [19] Santos, W. J.; Santiago, J. A.F.; Telles, J. C.F., An application of genetic algorithms and the method of fundamental solutions to simulate cathodic protection systems, Comput Model Eng Sci, 87, 23-40, (2012) [20] Atluri, S. N.; Shen, S., The meshless local Petrov-Galerkin (MLPG) method: a simple & less-costly alternative to the finite element and boundary element methods, Comput Model Eng Sci, 14, 11-51, (2002) [21] Wen, P. H., Meshless local Petrov-Galerkin (MLPG) method for wave propagation in 3D poroelastic solids, Eng Anal Bound Elem, 34, 315-323, (2010) [22] Wu, X. H.; Chang, Z. J.; Lu, Y. L.; Tao, W. Q.; Shen, S. P., An analysis of the convection-diffusion problems using meshless and meshbased methods, Eng Anal Bound Elem, 36, 1040-1048, (2012) · Zbl 1351.76086 [23] Fontes, E. F.; Santiago, J. A.F.; Telles, J. C.F., An iterative coupling between meshless methods to solve embedded crack problems, Eng Anal Bound Elem, 55, 52-57, (2015) · Zbl 1403.74103 [24] Barbosa, M.; Fontes, E. F.; Telles, J. C.F.; Santos, W. J., An efficient hybrid implementation of MLPGmethod, J Multiscale Model, 8, 1740002, (2017) [25] Konda, D. H.; Santiago, J. A.F.; Telles, J. C.F.; Mello, J. P.F.; Costa, E. G.A., A meshless reissner plate bending procedure using local radial point interpolation with an efficient integration scheme, Eng Anal Bound Elem, 99, 46-59, (2019) · Zbl 07006017 [26] Santos, W. J.; Santiago, J. A.F.; Telles, J. C.F., Using the gaussian function to simulate constant potential anodes in multiobjective optimization of cathodic protection systems, Eng Anal Bound Elem, 73, 35-41, (2016) · Zbl 1403.78035 [27] Golberg, M. A.; Chen, C. S., The theory of radial basis functions applied to the BEM for inhomogeneous partial differential equations, Bound Elem Commun, 5, 57-61, (1994) [28] Partridge, P.; Brebbia, C. A.; Wrobel, L. C., The dual reciprocity boundary element method, (1992), Computational Mechanics Publications: Computational Mechanics Publications Southampton · Zbl 0758.65071 [29] Golberg, M. A.; Chen, C. S., The method of fundamental solutions for potential, Helmholtz and diffusion problems, Boundary integral methods: numerical and mathematical aspects, vol. 1 of computational engineering, 103-176, (1999), Computational Mechanics Publications, WIT Press: Computational Mechanics Publications, WIT Press Boston, MA · Zbl 0945.65130 [30] Azevedo, J. P.S.; Wrobel, L. C., Nonlinear heat conduction in composite bodies: a boundary element formulation, Int J Numer Methods Eng, 26, 19-38, (1988) · Zbl 0633.65117 [31] Santos, W. J.; Santiago, J. A.F.; Telles, J. C.F., Optimal positioning of anodes and virtual sources in the design of cathodic protection systems using the method of fundamental solutions, Eng Anal Bound Elem, 46, 67-74, (2014) · Zbl 1297.65197 [32] Miltiadou, P.; Wrobel, L. C., Optimization of cathodic protection systems using boundary elements and genetic algorithms, Corrosion, 58, 11, 912-921, (2002) [33] Wendland, H., Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree, Adv Comput Math, 4, 389-396, (1995) · Zbl 0838.41014 [34] Garbow, B. S.; Hillstrom, K. E.; MorĂ©, J. J., MINPACK project, (1980), Argonne National Laboratory: Argonne National Laboratory Argonne, Illinois, USA [35] Nisancioglu, K., Predicting the time dependence of polarization on cathodically protected steel in seawater, Corrosion, 43, 100-111, (1987)
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